David Kinderlehrer

About

David Kinderlehrer is an Alumni Professor of Mathematical Sciences and a Professor of Materials Science and Engineering at Carnegie Mellon University. His research primarily focuses on applied mathematics and analysis, particularly partial differential equations. His work in applied mathematics, in collaboration with colleagues and postdoctoral researchers, is directed toward understanding the evolution of material microstructure, especially in polycrystalline microstructures composed of small crystallites or grains separated by grain boundaries. He has contributed to developing technologies for controlling grain arrangements to achieve desired material properties, utilizing experimental techniques and large-scale simulations. His discoveries include the grain boundary character distribution (GBCD), a statistical measure detailing texture evolution, which he explains through innovative analysis methods such as mass transport theory and entropy-based models. Additionally, his research explores the formation of non-random textures in materials and finds connections to information theory. Beyond materials science, his work extends to applications in cell biology, including intracellular transport mechanisms like protein motors and ion transport models such as the Poisson-Nernst Planck equations, heavily involving optimal transport theory.

Research topics

• Optics
• Mathematics
• Materials science
• Physics
• Pure mathematics
• Thermodynamics
• Mathematical economics
• Condensed matter physics
• Composite material
• Statistics

Selected publications

• A hybrid variational principle for the Keller–Segel system in ℝ²

  ESAIM Mathematical Modelling and Numerical Analysis · 2015-04-14 · 50 citations

  articleOpen access

  We construct weak global in time solutions to the classical Keller–Segel system describing cell movement by chemotaxis in two dimensions when the total mass is below the established critical value. Our construction takes advantage of the fact that the Keller–Segel system can be realized as a gradient flow in a suitable functional product space. This allows us to employ a hybrid variational principle which is a generalisation of the minimizing implicit scheme for Wasserstein distances introduced…

  PublisherOA PDFDOI

• A Wasserstein gradient flow approach to Poisson−Nernst−Planck equations

  ESAIM Control Optimisation and Calculus of Variations · 2015-09-15 · 31 citations

  articleOpen access1st authorCorresponding

  The Poisson−Nernst−Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of global weak solutions in a unified framework for the cases of both linear and nonlinear diffusion. The proof of the main results relies on the derivation of additional estimates based on the flo…

  PublisherOA PDFDOI

• Frustration and microstructure : an example in magnetostriction

  Research Showcase @ Carnegie Mellon University (Carnegie Mellon University) · 2018-06-29 · 22 citations

  articleOpen accessSenior author

  Abstract: "Microstructural properties of materials, especially crystalline solids, are implicated in many of their properties. Vice versa, there are macroscopic environments which limit microstructural configurations. Certain iron/rare earth alloys, eg, TbDyFeΓéé, display both a huge magnetostriction and frustration, i.e., minimum energy not achieved, in which microstructure plays an important, if puzzling, role. We discuss this example in the framework of continuum thermoelasticity theory, wher…

  PublisherOA PDFDOI

• The elementary defects of the Oseen-Frank energy for a liquid crystal

  Research Showcase @ Carnegie Mellon University (Carnegie Mellon University) · 2018-06-29 · 17 citations

  articleOpen access1st authorCorresponding

  Mathematics Technical Report

  PublisherOA PDFDOI

• Towards a gradient flow for microstructure

  Rendiconti Lincei Matematica e Applicazioni · 2017-11-15 · 15 citations

  article

  A central problem of microstructure is to develop technologies capable of producing an arrangement, or ordering, of a polycrystalline material, in terms of mesoscopic parameters, like geometry and crystallography, appropriate for a given application. Is there such an order in the first place? Our goal is to describe the emergence of the grain boundary character distribution (GBCD), a statistic that details texture evolution discovered recently, and to illustrate why it should be considered a mat…

  PublisherDOI

Recent grants

• Some Mesoscale Issues in Applied Mathematics

  NSF · $489k · 2003–2009

• Some mesoscale issues for applied mathematics

  NSF · $844k · 2008–2015

Frequent coauthors

• Shlomo Ta’asan

  Duke University

  31 shared

• Robert Hardt

  20 shared

• Xiang Xu

  Old Dominion University

  17 shared

• Gabor Ow

  Carnegie Mellon University

  16 shared

• Albert Cohen

  Michigan State University

  16 shared

• J Ikpitibo Clinton

  Carnegie Mellon University

  16 shared

• Robert B. Mason

  16 shared

• Harvey J. Stein

  Two Sigma Investments (United States)

  16 shared

Education

• Ph.D.

  University of California, Berkeley

• Other

  Scuola Normale Superiore, Pisa

Awards & honors

• Fellow of the American Mathematical Society
• SIAM Fellow

Similar researchers at Carnegie Mellon University

• Alan Friezeh-74
• Michael Youngh-57
• Irene Fonsecah-42